1. Preheat oven to 325°.
2. Melt 1 tablespoon butter. Pour into a 13 x 9inch glass or ceramic baking dish; tilt to coat bottom of dish. Top with onion.
3. Rub salt into chicken; arrange chicken over onion. Combine chayote, tomatillos, and serrano chiles; tuck between thighs. Scatter garlic over chicken; sprinkle with oregano.
4. Cut 1 tablespoon butter into pieces; scatter over dish. Cover; bake at 325° for 1 hour or until a thermometer registers 180°.
5. Uncover; bake 45 minutes, basting every 5 to 10 minutes.
6. Sprinkle cotija cheese over chicken; drizzle with basting juices. Bake 10 minutes. Top with cilantro; serve with lime wedges.